Example 2
Which of the following list of numbers does form an AP? If they form an AP, write the next two terms :
4, 10, 16, 22 ………………
Difference between 2nd and 1st term
= 10 – 4
= 6
Difference between third and second term
= 16 – 10
= 6
Difference between fourth and third term
= 22 – 16
= 6
Since difference is same, it is an AP
Common difference = d = 6
We have to find next two terms
We are given 4 terms .
So, we have to find 5th and 6th terms .
5th term = 4th term + common difference
= 22 + 6
= 28
6th term = 5th term + common difference
= 28 + 6
= 34
Hence 5th and 6th terms are 28 and 34.
Example 2
Which of the following list of numbers does form an AP? If they form an AP, write the next two terms :
(ii) 1, – 1, – 3, – 5, ……….
Difference between 2nd and 1st term = ( – 1) – (1)
= – 1 – 1
= – 2
Difference between 3rd and 2nd term = – 3 – ( – 1)
= – 3 + 1
= – 2
Difference between 4th and 3rd term = ( – 5) – ( – 3)
= – 5 + 3
= –2
Since difference is same, it is an AP
Common difference = d = –2
We have to find next two terms
We are given 4 terms .
So, we have to find 5th and 6th terms .
5th term = 4th term + common difference
= – 5 + ( – 2)
= – 5 – 2
= – 7
6th term = 5th term + common difference
= – 7 + ( – 2)
= – 7 – 2
= – 9
Hence the 5th and 6th term of the series are – 7 and – 9.
Example 2
Which of the following list of numbers does form an AP? If they form an AP, write the next two terms :
(iii) – 2, 2, – 2, 2, – 2, ………….
Difference between 2nd and 1st term
= 2 – ( – 2)
= 2 + 2
= 4
Difference between 3rd and 2nd term
= –2 – (2)
= –2 – 2
= –4
Since, difference is not same .
4 ≠ –4
Hence it is not an AP
Example 2
Which of the following list of numbers does form an AP? If they form an AP, write the next two terms :
(iv) 1, 1, 1, 2, 2, 2, 3, 3, 3, …………
Difference between 2nd and 1st terms = 1 – 1
= 0
Difference between 3rd and 2nd terms = 1 – 1
= 0
Difference between 4th and 3rd term = 2 – 1
= 1
Since difference is not same
0 ≠1
Hence it is not an AP.